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A328150 Number of n-bead necklace structures with no adjacent elements having the same color. 2


%S 1,0,1,1,3,3,12,24,103,387,1819,8933,48632,279484,1716523,11126025,

%T 76014437,544945399,4089010392,32025053060,261213946739,2214280580389,

%U 19471365925297,177319383231697,1669735890602062,16235408370162588,162796351456044465,1681427459283678177

%N Number of n-bead necklace structures with no adjacent elements having the same color.

%C Beads may be of any number of colors. Colors may be permuted without changing the necklace structure.

%C Equivalently, the number of set partitions of an n-set up to rotations where no block contains cyclically adjacent elements of the n-set.

%H Andrew Howroyd, <a href="/A328150/b328150.txt">Table of n, a(n) for n = 0..200</a>

%e a(6) = 12 because there are the following 12 necklace structures: ABABAB, ABABAC, ABABCD, ABACAD, ABACBC, ABACBD, ABACDC, ABACDE, ABCABC, ABCABD, ABCADE, ABCDEF.

%o (PARI) seq(n)={Vec(1 + intformal(sum(m=1, n, eulerphi(m) * subst(serlaplace(-1 + exp(-x + sumdiv(m, d, (exp(d*x + O(x*x^(n\m)))-1)/d))), x, x^m))/x))} \\ _Andrew Howroyd_, Oct 09 2019

%Y Row sums of A327396.

%Y Cf. A084423.

%K nonn

%O 0,5

%A _Andrew Howroyd_, Oct 05 2019

%E Terms a(16) and beyond from _Andrew Howroyd_, Oct 09 2019

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Last modified October 25 01:40 EDT 2021. Contains 348233 sequences. (Running on oeis4.)